For the broadcast version of this model, a.k.a. the \(\mathsf {BROADCAST~CONGESTED~CLIQUE}\)  model, in which the messages sent by a node in a certain round must all be identical, an \(\Omega (n/e^{O(\sqrt{\log {n}})}\log {n})\) -round lower bound on deterministic triangle detection is given by [1]}, through a reduction from 3-party number-on-forehead set disjointness.
